What is a good app for video editing?

I'm looking for some suggestions for a good video editing app for my phone, I don't need something super intricate to make some movie like video.
What I am looking for is an app that let's me take multiple videos and put them together into one.

Say I have 2 videos each 15 seconds long each.
I would like the capability to take a video, and say start it at the 5 second mark of one video, and the next video start it at the 10 second mark and combine.

Basically I want to be able to cut the video, then piece them together into a new one.

But really editing movies on a phone is really hard. The screen is way to small. Try using iMove on the Mac.

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They do, but I read some reviews that using iMovie saves videos permanently on the phone??

I understand that its pretty hard to edit, but I'm not looking to edit anything crazy. Just simple cuts from a video so I can combine multiple videos into one smaller one. I just didn't want to deal with uploading videos to a laptop and having to edit simply to put back into my phone.

If possible a free app would be preferable, but if it's a a good app with what I really want then I'd consider purchasing.

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